8 July 1994 Statistical model for tomographic reconstruction methods using spline functions
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Abstract
The conventional approach to tomographic reconstruction in the presence of noise consists in finding some compromise between the likelihood of the noisy projections and the expected smoothness of the solution, given the ill-posed nature of the reconstruction problem. Modelling noise properties is usually performed in iterative reconstruction schemes. In this paper, an analytical approach to the reconstruction from noisy projections is proposed. A statistical model is used to separate the relevant part of the projections from noise before the reconstruction. As reconstruction of sampled noise-free projections is still an ill- posed problem, a continuity assumption regarding the object to be reconstructed is also formulated. This assumption allows us to derive a spline filtered backprojection in order to invert the Radon operator. Preliminary results show the interest of combining continuity assumptions with noise modelling into an analytical reconstruction procedure.
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Habib Benali, Habib Benali, Jeanpierre V. Guedon, Jeanpierre V. Guedon, Irene Buvat, Irene Buvat, Melanie Pelegrini, Melanie Pelegrini, Yves J. Bizais, Yves J. Bizais, Robert Di Paola, Robert Di Paola, } "Statistical model for tomographic reconstruction methods using spline functions", Proc. SPIE 2299, Mathematical Methods in Medical Imaging III, (8 July 1994); doi: 10.1117/12.179255; https://doi.org/10.1117/12.179255
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